Timeline for Algebras whose subalgebras are finitely generated
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
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| Jan 22, 2020 at 19:43 | vote | accept | HeinrichD | ||
| Oct 30, 2016 at 20:46 | comment | added | HeinrichD | @KeithKearnes: This sounds good, especially because it is an adjective in contrast to ACC or maximal condition. | |
| Oct 30, 2016 at 20:45 | comment | added | HeinrichD | @YCor: Thank you. But "ascending chain condition" (ACC) seems to be more standard and refers to arbitrary partial orders. | |
| Oct 30, 2016 at 20:38 | comment | added | YCor | Probably there's no need for new terminology. For instance, Philip Hall (Finiteness conditions for soluble groups, 1954) refers to "the maximal condition for right ideals" (in a ring), "the maximal condition for subgroups" "the maximal condition for normal subgroups", etc. "The maximal condition for subalgebras" can also be found in old papers, e.g. this one: archive.numdam.org/ARCHIVE/CM/CM_1975__31_1/CM_1975__31_1_31_0/… | |
| Oct 30, 2016 at 20:13 | history | edited | Keith Kearnes | CC BY-SA 3.0 |
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| Oct 30, 2016 at 20:11 | comment | added | Keith Kearnes | I found a paper: Hereditarily Finitely Generated Commutative Monoids by J. C. Rosales and J. I. Garcı́a-Garcı́a, Journal of Algebra 221, 723-732 (1999). They use "hereditarily finitely generated" to mean a monoid whose submonoids are all finitely generated. This term might work for you. | |
| Oct 30, 2016 at 20:00 | history | edited | Keith Kearnes | CC BY-SA 3.0 |
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| Oct 30, 2016 at 19:44 | comment | added | HeinrichD | Thank you. This answers the terminology question. I would call this then "super finitely generated", since my question is not primarily about the property of being Noetherian. Notice that (i) -> (ii) needs that $k$ is Noetherian, but in their paper $k$ is just an alg. closed field. | |
| Oct 30, 2016 at 19:30 | history | edited | Keith Kearnes | CC BY-SA 3.0 |
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| Oct 30, 2016 at 19:12 | history | answered | Keith Kearnes | CC BY-SA 3.0 |